UPSI Digital Repository (UDRep)
|
![]() |
|
|
Abstract : Perpustakaan Tuanku Bainun |
Zika virus infection is a vector-borne disease transmitted by Aedes mosquitoes, with humans and mosquitoes as primary carriers. This research examines Zika virus transmission patterns and control measures using five mathematical models, employing dynamical systems stability theory, optimal control theory, and ODE45 numerical simulations. It initiates by investigating the effectiveness and details of increased medical investments, restricted access to infection zones and reducing human-mosquito exposure. Findings reveal that none of these measures alone can control the virus spread in the area. The first model is created by introducing a mosquito-harvesting measure, shown to be effective in reducing virus spread. However, caution is needed when applying this measure alone to prevent disproportionate consequences. Next, a Zika virus transmission model incorporating biodiversity dilution is created to analyze its regulatory role. The research findings indicate that biodiversity can suppress the rapid spread of viruses. Maintaining species abundance is beneficial for controlling the Zika virus. Building on this, the third model combines multiple measures in an optimal control framework to identify the best strategies. The fourth model we developed assesses a new infection pathway in Zika virus transmission. The findings reveals a clear enhancement effect in the early stages of transmission that diminishes over time. The fifth Zika virus transmission model focused on immigration, revealing immigration as a fundamental factor for the virus's long-term existence. Screening immigrants is critical for controlling outbreaks during large-scale outbreaks. Dynamic analyses were conducted on all models, identifying conditions and stability of disease-free and endemic equilibrium, emphasizing the critical role of the basic reproduction number in disease-free equilibrium stability. These findings have significant implications for public health strategies, suggesting that a combination of ecological management, immigration control, and targeted medical interventions is essential for controlling Zika virus transmission and informing policy decisions on disease management. |
References |
Agrawal, A., Gindodiya, A., Deo, K., Kashikar, S., Fulzele, P., et al. (2021). A Comparative Analysis of the Spanish Flu 1918 and COVID-19 Pandemics. The Open Public Health Journal,14(1),128-134. Agusto, F. B., Bewick, S., & Fagan, W. (2017). Mathematical model of Zika virus withverticaltransmission. Infectious Disease Modelling,2(2), 244-267. Agusto, F. B. & Bewick, S. (2017). Mathematical Model for Zika virus Dynamics WithSexualTransmissionRoute. Ecological Complexity,29,61-81. Ali, N. F. & Saadi, R. R. (2020). The Study of the Effect of Disease and Harvesting on Prey-Predator Interaction. Xinan Jiaotong Daxue Xuebao / Journal of Southwest Jiaotong University,55(1),1-8. Ali, H. M. & Ameen, I. G. (2021). Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions. Chaos, Solitons & Fractals,146,110864. Ayana, M., & Koya, P. R (2017). The Impact of Infective Immigrants on the Spread and Dynamics of Zika virus. American Journal of Applied Mathematics, 5(6), 145-153. Baril, C., Pilling, B. G., Mikkelsen, M. J., Sparrow, J. M., Duncan, C. A. M., et al. (2023). The influence of weather on the population dynamics of common mosquito vector species in the Canadian Prairies. Parasites & Vectors, 16(1), 153. Barredo, E., & DeGennaro, M. (2020). Not Just from Blood: Mosquito Nutrient Acquisitionfrom Nectar Sources. Trends in Parasitology,36(5),473-484. Bernoulli, D. (1760). Essai d'une nouvelle analyse de la mortalité causée par la petite vérole et des avantages de l'inoculation pour la prévenir. Mém. Mémoires de l'Académie Royale des Sciences de Paris, avec des mémoires de mathématique et de physique,1,1-45. Bhowmick, S., Gethmann, J., Conraths, F. J., Sokolov, I. M., & Lentz, H. H. K. (2020). Locally Temperature -Driven Mathematical Model of West Nile Virus SpreadinGermany. Journal of Theoretical Biology,488,110117. Bonds, J. A., Collins, C. M., & Gouagna, L. (2022). Could species-focused suppression of Aedes aegypti, the yellow fever mosquito, and Aedes albopictus , the tiger mosquito, affect interacting predators? An evidence synthesisfromtheliterature. Pest Management Science,78(7),2729-2745. Bonyah,E.,Khan, M.A., Okosun,KO, &Islam,S. (2017).ATheoreticalModel for ZikavirusTransmission. Plos One,12(10),e185540. Bosi, S., & Desmarchelier, D. (2020). Biodiversity, Infectious Diseases, and the DilutionEffect. Environmental Modeling and Assessment,25,277-292. Basiao, Z. U., Doyle, R. W., & Arago, A. L. (1996). A statistical power analysis of the ‘internal reference’ technique for comparing growth and growth depensationof tilapiastrains. Journal of Fish Biology,49(2),277-286. Boushehri, R., Motamed, R., Ellison, K., & Stanton, K. (2022). Estimating epistemic uncertaintyin soilparameters for nonlinear site response analyses: Introducing the Latin Hypercube Sampling technique. Earthquake Spectra, 38(4), 2422-2450. Calvet, G. A., Kara, E. O., Bôtto-Menezes, C. H. A., Da Costa Castilho, M., De Oliveira Franca, R. F., et al. (2023). Detection and persistence of Zika virus in body fluids and associated factors: A prospective cohort study. Scientific Reports,13(1),21557. Caminade, C., Turner, J., Metelmann, S., Hesson, J. C., Blagrove, M. S., Solomon, T., et al. (2017). Global Risk Model for Vector-Borne Transmission of Zika virus Reveals the Role of El Niño 2015. Proceedings of the National Academy of Sciences of the United States of America,14(1), 119-124. Castillo-Chevez, C., & Thieme, H. R. (1995). Asymptotically Autonomous Epidemic Models, Mathematical Population Dynamics: Analysis of Heterogeneity. Theory of Epidemics,1,33-50 Cator, L. J., Johnson, L. R., Mordecai, E.A., El Moustaid, F., Smallwood, T. R. C., et al. (2020). The Role of Vector Trait Variation in Vector-Borne Disease Dynamics. Frontiers in Ecology and Evolution,8,189. Da ConceiçãoAraújo, D.,DosSantos,A. D.,Lima,S. V. M.A.,Vaez,A. C.,Cunha, J. O., et al. (2020). Determining the association between dengue and social inequality factors in north-eastern Brazil: A spatial modelling. Geospatial Health,15(1),70-79. David, M. R., Maciel-de-Freitas, R., Petersen, M. T., Bray, D., Hawkes, F. M., et al. (2023). Aedes aegypti oviposition-sites choice under semi-field conditions. Medical and Veterinary Entomology,37(4),683-692. De Almeida Oliveira Evangelista, G., Hughes Carvalho, R., Sant’Ana Menezes, G., Carvalho De Abreu, Y., Sardi, S. I., et al. (2021). Meningoencephalitis Associated with Zika Virus and Chikungunya Virus Infection. Japanese Journal of Infectious Diseases,74(6),584-586. Duclos, T., & Reichert, T. (2022). A Solution to the Kermack and McKendrick Integro-Differential Equations.Preprint, Epidemiology. Du, S., Liu, Y., Liu, J., Zhao, J., Champagne, C., Tong, L., et al. (2019). Aedes Mosquitoes Acquire and Transmit Zika virus by Breeding in Contaminated AquaticEnvironments. Nature Communications,10(1), 1324. Duve, P., Charles, S., Munyakazi, J., Lühken, R., &Witbooi, P. 2023.Amathematical model for malaria disease dynamics with vaccination and infected immigrants. Mathematical Biosciences and Engineering,21(1),1082-1109. Emzir, M. F., Woolley, M. J., & Petersen, I. R. (2022). Stability analysis of quantum systems: A Lyapunov criterion and an invariance principle. Automatica, 146, 110660. Ferguson, N. M., Cucunubá, Z. M., Dorigatti, I., Nedjati-Gilani, G. L., Donnelly, C. A., Basáñez, M., et al. (2016). Countering the Zika Epidemic in Latin America. Science,353(6297), 353-354. Fleming, W. H., & Rishel, R. W. (1975). Deterministic and Stochastic Optimal Control.NewYork.:SpringerVerlag. Glatter, K. A., & Finkelman, P. (2021). History of the Plague: An Ancient Pandemic for the Age of COVID-19. The American Journal of Medicine, 134(2), 176-181. Goodman,A. (2020). The Global Impact of the ZikaVirus Pandemic:The Importance ofEmergency Preparedness. Health,12(02),132-140. Guanche Garcell, H., Gutiérrez García, F., Ramirez Nodal, M., Ruiz Lozano, A., Pérez Díaz, C. R., et al. (2020). Clinical relevance of Zika symptoms in the context of a Zika Dengue epidemic. Journal of Infection and Public Health, 13(2),173-176. Hackbush W. (1978). A Numerical Method for Solving Parabolic Equations with OppositeOrientations. Computing,20(3):229–40. Halliday, F. W., Rohr, J. R., & Laine, A. (2020). Biodiversity loss underlies the dilution effect of biodiversity. (J. Chase, Ed.) Ecology Letters, 23(11), 1611-1622. Han, Q. X. (2019). Dynamics of the Stochastic Population Model. Beijing, China: Science Press. Heidecke, J., Lavarello Schettini, A., & Rocklöv, J. (2023). West Nile virus eco-epidemiology and climate change. (S. Paz, Ed.)PLOS Climate, 2(5), e0000129. Hilker, F. M., & Liz, E. 2020. Threshold harvesting as a conservation or exploitation strategyinpopulationmanagement. Theoretical Ecology,13(4),519-536. Huang, J., Ruan S., & Yu P. (2019). Bifurcation Analysis of a Mosquito Population Model with a Saturated Release Rate of Sterile Mosquitoes. SIAM Journal on Applied Dynamical Systems,18(2), 939-972. Jones, R., Kulkarni, M. A., Davidson, T. M. V., RADAM-LAC Research Team, & Talbot, B. (2020). Arbovirus vectors of epidemiological concern in the Americas: A scoping review of entomological studies on Zika, dengue and chikungunya virusvectors. (A. M. Samy,Ed.)PLOS ONE,15(2),e0220753. Jorge, F.A.,Thomazella M. V., Moreira D. D. C., Lopes L. D. G.,Teixeira J. J. V. et al. (2020). Evolution and Upcoming on Zika virus Diagnosis Through an Outbreak:ASystematic Review. Reviews in Medical Virology,30,10-1002. Kermack, W. O., & Mckendrick A. G. (1927). A Contribution to the Mathematical Theory of Epidemics. Proceedings of The Royal Society A Mathematical Physical and Engineering sciences,115(772), 700-721. Kermack, W. O., & McKendrick A. G. (1933). Contributions to the Mathematical Theory of Epidemics-III. Further Studies of the Problem of Endemicity. Proceedings of The Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character,141(843),94-122. Khan, M. A., Shah, S. W., Ullah, S., & Gómez-Aguilar, J. F., (2019). A Dynamical Model of Asymptomatic Carrier Zika virus With Optimal Control Strategies. Nonlinear Analysis: Real World Applications, 50,140-170. Kharab, A., & Guenther, R. B. (2023). An introduction to numerical methods: A MATLAB approach (Fifth edition). Boca Raton,FL,C&H/CRCPress. Kucharski, A. J., Funk S., Eggo R. M., Mallet H. P., Edmunds W. J., & Nilles, E. J. (2016). Transmission Dynamics of Zika virus in Iisland Populations: A Modelling Analysis of the 2013-2014 French Polynesia Outbreak. PLOS Neglected Tropical Diseases,10(5), e0004726. Lakhani, K. H., & Service, M. W. (1974). Estimated Mortalities of the Immature Stages of Aedes Cantons (Mg.) (Diptera, Culicidae) in a Natural Habitat. Bulletin of Entomological Research,64(2), 265-276. Lasalle, J. P. (1976). The stability of dynamical systems, Society for Industrial and AppliedMathematics. Lee, L.W., & Mohd, M.H. (2020). The Biodiversity Effect in Regulating the Prevalence of Sin Nombre Virus (SNV). Malaysian Journal of Fundamental and Applied Sciences,16,271-276. Leonhard, S. E., Halstead, S., Lant, S. B., Militão De Albuquerque, M. D. F. P., De Brito, C. A. A., et al. (2021). Guillain-Barré syndrome during the Zika virus outbreak in Northeast Brazil: An observational cohort study. Journal of the Neurological Sciences,420,117272. Lenhart, S., & Workman, J.T. (2007), Optimal control applied to biological models. London:Taylor &Francis Group. Li, Y., Liu, X., Yuan, Y., Li, J., & Wang, L. (2022). Global Analysis of Tuberculosis Dynamical Model and Optimal Control Strategies Based on Case Data in the UnitedStates. Applied Mathematics and Computation,422,126983. Luis, A. D., Kuenzi, A. J., & Mills J. N. (2018). Species Diversity Concurrently Dilutes and Amplifies Transmission in a Zoonotic Host-Pathogen System Through Competing Mechanisms. Proceedings of the National Academy of Sciences,15(31), 7979-7984. Malla, A., Shanmugaraj, B., & Ramalingam, S. (2019). Emerging mosquito-borne arboviral infection Zika -An epidemiological review. Asian Pacific Journal of Tropical Biomedicine,10(5),193-200. Manore, C. A., Hickmann, K. S., Xu, S., Wearing, H. J., & Hyman, J. M. (2014). Comparing Dengue and Chikungunya Emergence and Endemic Transmission ina.AegyptiAnda.Albopictus. Journal of Theoretical Biology,356,174-191. Martheswaran, T. K., Hamdi, H., Al-Barty, A., Zaid, A. A., & Das, B. (2022). Prediction of dengue fever outbreaks using climate variability and Markov chain Monte Carlo techniques in a stochastic susceptible-infected-removed model. Scientific Reports,12(1),5459. Martin, E., Medeiros, M. C. I., Carbajal, E., Valdez, E., Juarez, J. G., Garcia-Luna, S., et al. (2019). Surveillance of Aedes Aegypti Indoors and Outdoors Using Autocidal Gravid Ovitraps in South Texas During Local Transmission of Zika virus,2016to2018. Acta Tropica,192,129-137. Minwuyelet, A., Petronio, G. P., Yewhalaw, D., Sciarretta, A., Magnifico, I., et al. (2023). Symbiotic Wolbachia in mosquitoes and its role in reducing the transmission of mosquito-borne diseases: Updates and prospects. Frontiers in Microbiology,14,1267832. Miyaoka, T. Y., Lenhart, S., & Meyer, J. F. C. A. (2019). Optimal Control of Vaccinationin aVector-Borne Reaction–Diffusion ModelAppliedto Zika virus. Journal of Mathematical Biology,79(2),1077-1104. Momoh,A. A., & Fügenschuh, A. (2018). Optimal Control of Intervention Strategies and Cost Effectiveness Analysis for a Zika virus Model. Operations Research for Health Care,18,99-111. Muhammad Khan, F., Ali, A., Ullah Khan, Z., Alharthi, M. R., & Abdel-Aty, A.-H. (2021). Qualitative and Quantitative studyof Zika virus epidemic model under Caputo’sfractionaldifferential operator. Physica Scripta,96(12),124030. Ngonghala, C. N., Ryan, S. J., Tesla, B., Demakovsky, L. R., Mordecai, E. A., et al. (2021). Effects of changes in temperature on Zika dynamics and control. Journal of The Royal Society Interface,18(178),20210165. Olaniyi, S., Okosun, K.O., Adesanya, S.O., & Areo, E.A. (2018). Global Stability and Optimal ControlAnalysis of Malaria Dynamics in the Presence of Human Travelers. Open Infectious Diseases Journal,10(1), 166-186. Osorio, L., Parra, B., Moyano, M., Lopez-Gonzalez, R., Jimenez-Arango, J. A., et al. (2024). Guillain-Barré Syndrome after the Zika Epidemic in Colombia: A Multicenter, Prospective, Matched Case-Control Study.Preprint. Pal, A. K., Bhattacharyya, A., & Mondal, A. (2022). Qualitative analysis and control of predator switching on an eco-epidemiological model with prey refuge and harvesting. Results in Control and Optimization,7,100099. Patil, R.R., Kumar, C.S., & Bagvandas, M. (2017). Biodiversity Loss: Public Health Risk of Disease Spread and Epidemics. Annals of Tropical Medicine and Public Health,10,1432-1438. Peixoto, I. D. & Abramson G. (2006). The Effect of Biodiversity on the Hantavirus Epizootic. The Ecological Society of America,87(4),873-879. Peeters, B., Grøtan, V., Gamelon, M., Veiberg, V., Lee, A. M., et al. (2022). Harvesting can stabilize population fluctuations and buffer the impacts of extremeclimaticevents. (S. Munch, Ed.) Ecology Letters,25(4),863-875. Pielnaa, P., Al-Saadawe, M., Saro, A., Dama, M. F., Zhou, M., et al. (2020). Zika virus-spread, epidemiology,genome, transmissioncycle, clinicalmanifestation, associated challenges, vaccine and antiviral drug development. Virology, 543, 34-42. Prist, P. R., Prado,A.,Tambosi, L. R., Umetsu, F., DeArruda Bueno,A., et al. (2021). Moving to healthier landscapes: Forest restoration decreases the abundance of Hantavirus reservoir rodents in tropical forests. Science of The Total Environment,752:141967. Pontryagin, L. S. (1962). The Mathematical Theory Of Optimal Processes: John Wiley&Sons,Inc. Raquel, B. C., Karla, G., Sergio, O., Victor, Z. J., Nery, S., Cristhiam, C. C.,et al. (2018). Zika virus Infection in Nicaraguan Households. Plos Neglected Tropical Diseases,12(5), e6518. Renardy, M., Hult, C., Evans, S., Linderman, J. J., & Kirschner, D. E. (2019). Global sensitivity analysis of biological multiscale models. Current Opinion in Biomedical Engineering,11,109-116. Revelle, C. S., Lynn, W. R., & Feldmann, F. (1967). Mathematical Models for the EconomicAllocation ofTuberculosis ControlActivities in Developing Nations. American Review of Respiratory Disease,96(5),893. Ross,R. (1911). The Prevention of Malaria (2ed.). London:Murray. Sadeghieh, T., Sargeant, J. M., Greer, A. L., Berke, O., Dueymes, G., et al. (2021). Zika virus outbreak in Brazil under current and future climate. Epidemics, 37, 100491. Salkeld, D., Hopkins, S., & Hayman, D. (2023). Emerging infectious diseases and globalization—Travel, trade, and invasive species. Emerging Zoonotic and Wildlife Pathogens (1sted.),175-198.OxfordUniversityPressOxford. Savatorova, V. (2023). Exploring Parameter Sensitivity Analysis in Mathematical ModelingwithOrdinary Differential Equations. CODEE Journal,16(1),1-26. Sbarra, A. N., Mosser, J. F., Jit, M., Ferrari, M., Ramshaw, R. E., et al. (2023). Estimating national-level measles case–fatality ratios in low-income and middle-income countries: An updated systematic review and modelling study. The Lancet Global Health,11(4),e516-e524. Supriyono, Kuwata, R., Torii, S., Shimoda, H., Ishijima, K., et al. (2020). Mosquito-borne viruses, insect-specific flaviviruses (family Flaviviridae, genus Flavivirus), Banna virus (family Reoviridae, genus Seadornavirus), Bogor virus (unassigned member of family Permutotetraviridae), and alphamesoniviruses 2 and 3 (family Mesoniviridae, genus Alphamesonivirus) isolated from Indonesian mosquitoes. Journal of Veterinary Medical Science, 82(7),1030-1041. Sousa, R. S. de, Menezes, L. G. C. de, Felizzola, J. F., Figueiredo, R. de O., Sá, T. D. de A., & Guerra, G. A. D. (2016). Water and Health in Igarapé-Açu, Pará, Brazil. Saúde E Sociedade,25(4), 1095-1107. Stoddard, P. K. (2018). Managing Aedes Aegypti Populations in the First Zika Transmission Zones in the Continental United States. Acta Tropica (187), 108-118. Strugarek, M., Bossin, H., & Dumont, Y. (2019). On the Use of the Sterile Insect Release Technique to Reduce or Eliminate Mosquito Populations. Applied Mathematical Modelling,68,443-470. Takimoto, G., Shirakawa, H., & Sato, T. (2022). The Relationship between Vector Species Richness and the Risk of Vector-Borne Infectious Diseases. The American Naturalist,200(3),330-344. Talaga, S., Dejean, A., Mouza, C., Dumont, Y., & Leroy, C. (2018). Larval Interference Competition Between the Native Neotropical Mosquito Limatus Durhamii and the InvasiveAedesAegypti Improves the Fitness of Both Species. Insect Science: English version,025(006), 1102-1107. Teng, Z. D., & Zhang, L. (2022). Stability Theory and Application of Ordinary Differential Equations.Beijing,China:Science press. Thieme, H. R. (1992). Convergence Results and a Poincar & Bendixson Trichotomy for Asymptotically Autonomous Differential Equations. Journal of Mathematical Biology,30,755-763. Traoré, A. (2020). Analysis of a Vector-Borne Disease Model with Human and Vectors Immigration. Journal of Applied Mathematics and Computing, 64, 411-428. Ukanwoke, N. O., Okuonghae, D., & Inyama, S. C. 2022. Modelling the dynamics of Zika in a population with two strains of the virus with optimal control and cost-effectiveness analysis. International Journal of Dynamics and Control, 10(3),956-980. Van den Dreessche P., & Watmough, J. (2002). Reproduction Numbers and Sub-threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences,180,29-48. Van De Straat, B., Sebayang, B., Grigg, M. J., Staunton, K., Garjito, T. A., et al. (2022). Zoonotic malaria transmission and land use change in SoutheastAsia: Whatisknownaboutthe vectors. Malaria Journal,21(1),109. Vinter, R. (2020). Optimal Control and Pontryagin’s Maximum Principle. In J. Baillieul & T. Samad (Eds.), Encyclopedia of Systems and Control,1-8. London:Springer London. Wang, L., & Zhao, H. (2021). Modeling and DynamicsAnalysis of ZikaTransmission WithContaminatedAquatic Environments. Nonlinear Dynamics,104,845-862. Wang,W. M.,&Cai,Y. L. (2020). Biomathematic Model Pattern Dynamics.Beijing, China:Science Press. Wilder-Smith, A., Chiew, C. J., & Lee, V. J. (2020). Can we contain the COVID-19 outbreak with the same measures as for SARS? The Lancet Infectious Diseases,20(5),e102-e107. Wilke,A. B. B., Mhlanga,A., Kummer,A. G.,Vasquez,C., Moreno, M., et al. (2023). Diel activity patterns of vector mosquito species in the urban environment: Implications for vector control strategies. (G. Rasic, Ed.)PLOS Neglected Tropical Diseases,17(1),e0011074. Witbooi, P., Abiodun, G., & Nsuami, M.,(2021). A model of malaria population dynamics with migrants. Mathematical Biosciences and Engineering, 18(6), 7301-7317. Witbooi, P. J. (2021). An SEIR model with infected immigrants and recovered emigrants. Advances in Difference Equations,2021(1),337. WHO. Zika virusfacts. Retrievedfrom http://www.who.int/mediacentre/factsheets/zika/en/ WHO,Globalvector controlresponse 2017-2030.Retrieved from https://www.who.int/publications/i/item/9789241512978. Xu, R.,Tian, X. H., & Gan, Q. T., (2019). Mathematical Modeling and Analysis on the Dynamics of Infectious Diseases.Beijing,China:Science Press. Xu, Y., Zhou, J., Liu, T., Liu, P., Wu, Y., et al. (2022). Assessing the risk of spread of Zika virus under current and future climate scenarios. Biosafety and Health, 4(3),193-204. Yakob, L. (2022). Zika Virus after the Public Health Emergency of International Concern Period,Brazil. Emerging Infectious Diseases,28(4),837-840. Yamazaki, K. (2019). Zika virus Dynamics Partial Differential Equations Model WithSexualTransmission Route. Nonlinear Analysis: Real World Applications, 50,290-315. Yavuz, M., & Sene, N. (2020). Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate. Fractal and Fractional,4(3),35. Yin H., Yang, C., & Zhang, X. (2018). Dynamics of Malaria Transmission Model WithSterileMosquitoes. Journal of Biological Dynamics,12(1),577-595. Yuan B., & Wang J. (1997). Compensatory Effects in Plants After Herbivore Feeding. Journal of Ecology (in Chinese),1997,16(6), 41-45. Yusof, F. M., MD. Ismail, A. I. & Ali, N. M. (2010). Modeling Population Harvesting of Rodents for the control of Hantavirus Infection. Sains Malaysiana,39(6), 935-940. Yusof, F. M., Azmi, A., Mohd, M. H. & MD Ismail. A. I. (2018). E.ect of Biodiversity on the Spread of Leptospirosis Infection. Paper presented at the In Proceedings of the International Conference on Mathematical Sciences and Technology 2018 (MathTech 2018), 10-12 December 2018., The Hotel Equatorial Penang, Malaysia. Yusof, F. M., Abdullah, F. A. & MD Ismail, A. I. (2019). Modeling and Optimal ControlontheSpread ofHantavirus infection. Mathematics (1192),1-11. Zanluca, C., Melo, V. C., Mosimann,A. L., Santos, C. N., Luz, K. (2015). First report of autochthonous transmission of Zika virus in Brazil, Memórias do Instituto Oswaldo Cruz ,110(2015),569-572. Zerfu, B., Kassa, T., & Legesse, M. (2023). Epidemiology, biology, pathogenesis, clinical manifestations, and diagnosis of dengue virus infection, and its trend in Ethiopia:Acomprehensive literature review. Tropical Medicine and Health, 51(1),11. Zhang, S. Q. (2002). Approach on the Fitting Optimization Index of Curve Regression, Chinese Journal of Health Statistics (in Chinese),19(1), 9-11.
|
This material may be protected under Copyright Act which governs the making of photocopies or reproductions of copyrighted materials. You may use the digitized material for private study, scholarship, or research. |